"The best and safest thing is to keep a balance in your life, acknowledge the great powers around us and in us. If you can do that, and live that way, you are really a wise man."
On the other hand, I know many people who were coddled their whole lives and as a result, they don't know how to be an adult. Instead of slowly learning to be more and more independent, these people have a learned behavior of "it's okay; someone else will do it for me if I can't." When raised like this, people often grow up to be lazy adults or tend to buckle at the smallest sign of adversity. Being enabled your whole life can make it difficult to make big decisions for yourself and when the time comes where there no longer someone to do things for you or get you out of tough situations, you're screwed because it is a skill set that you never developed.
Independence is a very important skill to learn, but there is also something to be said for being able to recognize your own strengths and weaknesses and knowing where your limits are. Fostering independence helps one gain self-esteem and learn the value of perseverance. In my personal life, I have known a few people who have been in physically and/or emotionally abusive relationships and a common thread that often appears is low self-esteem. If you are independent and have confidence in yourself, it is a lot harder for someone else to treat you like a pile of dirt and make you feel as though you don't deserve any better or that you can't make it without them.
Though I write this as a woman, I am going to speak for both genders and say that I believe there is a push to be independent (regardless of your gender) but it is my opinion that the reason or source is not the same, and that it is also largely dependent on the type of household you were raised in and what generation you are a part of. For women, I think there is a historical piece to the modern day, "independent woman" stereotype. It's almost as though we must show that we (as a gender) don't need the support of a man, since in the past there were many things that women weren't allowed to do. I still believe there is a societal pressure for men to be the caretaker, not only for himself, but for the whole family. I was brought up to believe it is shameful if a man isn't able to be "The Provider" in a household.
I used to be someone (much like my mother) who flat-out refused to accept any type of assistance- the whole "bite your nose off to spite your face" scenario- and viewed asking for help (or even appearing as though you may need help) as a sign of great weakness. Through my own attempts at self-awareness and many years of therapy, I have tried to stray from this dichotic view of adulthood and independence. Now that I am a parent myself, I try to gently encourage my children to be independent and do things for themselves, while at the same time showing them that there is no shame in asking for help when you need it.
To me, the bottom line is that you have to learn some form of moderation (just like with most things in life). As far as gender roles and independence, I think we should try to move further from that deep-rooted push to be "The Provider" or "The Independent Woman" and learn to work together as a team, rather than as a strong individual. You can be "too independent". One must always keep in mind though that it is human nature to look out for oneself first and foremost, so you mustn't put all your eggs in one basket, so to speak. Why should someone else break their back to help you if you're not willing to shoulder any of the load? If you want help, you have to help yourself.